DISTRIBUTION OF SOLUBLE AND INSOLUBLE CHEMICAL SPECIES OF CHROMIUM (III) AND (VI) IN AQUEOUS SOLUTIONS

Abstract. On the basis of currently revised thermodynamic data for Cr(III) and Cr(VI) hydrolysis and photolytic equilibria in addition to original thermodynamic and graphical approach, used in this paper, the repartition of their soluble and insoluble chemical species has been investigated. By means of the diagrams “ΔG – pH”, the areas of thermodynamic stability of chromium(III) hydroxide have been established for a number of the analytical concentration of Cr(III) in heterogeneous mixtures. The degree of polynuclearity for Cr (III) and Cr(VI) has been calculated for different initial composition of aqueous solutions. The diagrams of heterogeneous and homogeneous chemical equilibria have been used for graphical representation of complex equilibria in aqueous solutions containing Cr(III) and Cr(VI). The obtained calculated results correlate well with existing experimental data.


Introduction
The increased knowledge regarding the behavior of chromium in natural waters and soils is essential for the complete and accurate determination of its possible toxicity to the particular ecosystem, as well as for the development of methods which minimize the risk of pollution areas.Due to the complex, heterogeneous nature of the soil and surface waters, the determination of the chromium behavior may be a very diffi cult task.Only by understanding the specifi c mechanism of the reactions, in which chrome may participate, one can expect a truthful forecast of its behavior.
Chromium (Cr) is one of the most strategically important materials in the world, having a wide range of applications in metallurgy and chemical industry.Alloys containing chromium metal enhance such properties as the resistance, stability to corrosion and oxidation.Furthermore, chromium is used as an additive in the production of stainless steel, in the treatment of leather, metal plating, in the production of catalysts and in other industries [1].
Chromium is rarely found in nature as a free metal.Chromium can exist in all degrees of oxidation from 0 to VI.The most typical chromium degrees of oxidation are +2, +3 and +6, but +3 and +6 are most stable ones, while the oxidation states +1, +4 and +5 are rare found in nature.Cr(III) is much less toxic than Cr(VI) [3].Cr(III) is the most stable form in the environment and biological systems.It is an essential trace element in the human body and participates, in combination with various enzymes, in the metabolism of sugars, proteins and fats.The recommended daily dose for an adult is between 0.5 to 1.0 mg/day [4].
According to the World Health Organization (WHO) and the International Agency for Research on Cancer Cr(VI) is a carcinogen form.The inhalation of Cr(VI) can cause irritation of the nose and nosebleeds.After the contact of Cr(VI) with the human body, skin rashes, indigestion and ulcers, respiratory diseases, weakness of immune system, kidney and liver damage, alteration of genetic material, lung cancer and death may appear or be caused [5].The WHO considers Cr(VI) as a pollutant of main concern.The concentration of 0.05 mg/L for Cr(VI) has been adopted as the maximum allowable concentration (MAC) for drinking water.That is why a constant monitoring and analysis of chromium in the environment is becoming a requirement.The natural sources of chromium in natural waters are such processes as erosion of rocks and run-off from the land-based systems.The chromium concentration in rivers and lakes is generally limited to 0.5 -100.0 μg/L [6], while in marine waters it ranges between 0.156-0.260μg/L [7].
The concentration of chromium in contaminated area may be much higher.The local increase in the concentration of chromium in waters (mainly in rivers) is due to wastewater discharges from the metallurgy, electroplating, chemical and leather industries, as well as the health leach dumps etc.The concentration and type of substances present in the effl uent depend on the nature of industrial processes using chromium [8].
In natural waters, chromium exists in only two stable states, Cr(III) and Cr(VI).The presence and the ratio between these two forms dependent on the various processes that include chemical, photochemical, and redox processes, reactions of precipitation/dissolution and adsorption/desorption.The high concentrations of chromium in the nature cause mutagenic, teratogenic or carcinogenic effects.
The highest concentration of chromium in the Chisinau city was found in samples of snails collected in the industrial zone, indicating a strong pollution of nearby territory by this metal (snails were collected in the vicinity of the factory of leather processing "Piele SA") and near the gas station [9].A relatively high concentration of chromium was detected in immature specimens of Helix Lutescens (2.0 μg/g).The Cr concentration in the soil in the industrial area was particularly high -1079.7 μg/g.The aim of this paper is the thermodynamic analysis, based on the selected recent experimental data, and graphical representation of the distribution of various soluble and insoluble chemical forms of chromium (III) and (VI) for different concentrations in a wide range of pH values.

Theoretical part Thermodynamic calculations and graphic representation of the distribution of chemical forms of Cr(III) and Cr(VI)
In this paper the diagrams of heterogeneous chemical equilibria (DHCE) have been used for graphical representation of complex equilibria in aqueous solutions containing Cr(III) [10].Their construction is based on the determination of the thermodynamic stability areas of the solid phase [11][12][13], derived by the method of residual concentrations (RC) [14,15].The biphasic systems consisting of the soil solution and minerals, in which a number of chemical reactions occur simultaneously, are heterogeneous systems.These diagrams are similar in appearance to the distribution diagram in the case of homogeneous (single-phase) systems [16], however, the principle of their construction differs signifi cantly from the past ones.
Besides the process of chromium hydroxide Cr(OH) 3(S) dissolution (the subscript symbol "S" denotes solid phase): the hydrolysis reaction with the formation of mono-and polynuclear hydroxocomplexes Cr i (OH) j 3i-j are taken into account [17]: Near to the equations of reactions their corresponding equilibrium constants K S and K ij are written.The conditions of mass balance (MB) in this system are formulated on the basis of residual concentrations, RC [14,15]: For convenience, the notation of species charges is omitted.The quantities C 0 i and C r i in Eq.(3) and Eq.( 4) represent, respectively, the analytical (total) and residual concentrations of the "i" component in the heterogeneous system under consideration.In Eq.(3) and Eq.( 4) by ΔC i the amount of solid phase in one liter of solution is denoted.In Eq.( 4), C 0 H symbolizes the excess of the H + ions towards the hydroxyl ions in the two-phase mixture, C 0 H = -C 0 OH .From the stoichiometric composition of chromium hydroxide Cr(OH) 3(S) , the following relation is derived: Moreover, in the framework of the RC method, it can be written: ΔC OH = -ΔC H and C r OH = -C r H .The equilibrium concentration of chromium ion [Cr 3+ ] is determined from the equilibrium constant K S (Eq.( 1)).In view of the law of mass action (LMA) and relation (5), from the mass balance (3) and (4) at a given pH, we obtain an equation with one unknown -ΔC Cr , which can be easily solved by the known numerical methods.From the combined aforementioned equations of LMA and MB, one can calculate the distribution diagram of the chromium ion in the solid phase and complex species in the liquid phase (aqueous solution), i.e. the DHCE.The following equations for calculating the partial molar fraction of species f i in the heterogeneous system, wherein the reactions (1) and (2) proceed simultaneously, have been used Here the subscript "tot" means the sum of the molar fractions of all the soluble species.On the basis of Eq.(3), Eq.( 5) and Eq.( 6) the validity of the following equation can be verifi ed: (7) When i > 1 for the hydroxo-complexes of type Cr i (OH) j , the polynuclear complexes are formed.In order to appreciate their amount, the degree of the polynuclear hydroxo-complex formation has been calculated [18]: If P > 1, then the polynuclear hydroxo-complexes are present in the solution.
In appearance DHCE are similar to the diagrams of distribution of the species in homogeneous solution.The latter are usually built in the coordinates f i (pH), as in the absence of polynuclear complexes, the molar fractions of species f i in aqueous solution are a function of the solution pH and do not depend on the initial concentrations of components.In the case of heterogeneous equilibria, the molar fractions of species depend also on the initial composition of the mixture, being at a given pH a function of one variable f i = f(C 0 (Cr)).In this case, it is desirable to build the diagrams in the coordinates (f i , pH), fi xing the values of other variables.The procedure for constructing DHCE includes the following successive steps: 1) Thermodynamic calculation of the Cr(OH) 3(S) stability area.The authors [9][10][11][12][13] derived the equation for calculating the Gibbs energy of complex process ΔG S,tot , in which reactions ( 1) and ( 2) occur simultaneously: The solid phase Cr(OH) 3(S) is stable if ΔG S,tot > 0. The condition ΔG S,tot = 0 corresponds to the beginning of its dissolution (or precipitation).
2) Subsequently, the molar fractions f i of all the chemical species containing chromium ion are calculated by the Eq.( 6) within the stability area of Cr(OH) 3(S) defi ned in the previous stage.
3) For completeness, outside this area, i.e. for homogeneous aqueous solutions, the molar fractions are calculated by the usual equations for the distribution diagrams [16].In this case, the f value does not depend on the initial concentrations of examined components under the conditions of formation of only mononuclear complex species.
Distribution diagrams of chemical forms Cr(VI) are calculated by the usual equations for the distribution in the homogeneous systems.The chemical equilibria and their equilibrium constants, used in this paper, are given in Table 1.

Results and discussion
The data regarding the thermodynamic stability of the chromium (III) hydroxide, calculated by Eq.( 9), are depicted graphically on the Figure 1.As one can see, the area of predominance of the solid phase diminishes noticeably with decreasing the analytical concentration of Cr(III) in the heterogeneous mixture.

5+
. Figure 2 shows DHCE for C 0 (Cr) = 10 -6 М. Hence one can conclude that Cr 3+ exists only in highly acidic environments, Cr(OH) 2+ predominates at the рН values of 3.7 -6.0, while the solid phase Cr(OH) 3(S) is prevailing at pH > 6.0.In highly alkaline solutions, at pH > 12, chromium in the solution is in the anionic form of hydroxocomplex Cr(OH) 4 -.By increasing the analytical concentration of Cr(III) the amount of its polynuclear hydroxocomplexes grows substantially (Figures 3 and 4).By comparison Figures 3 and 4  On the Figure 5 the degree of polynuclear complex formation for Cr(VI) at its different analytical concentrations is represented.As one can see, the polynuclear Cr(VI) species are not formed at the concentration C 0 (Cr) ≤ 10 -5 M.
Cr(VI) may be present in the aqueous solution mainly in the form of chromate, dichromate, hydrogen chromate, chromic acid and hydrogen dichromate.The last two species were found only in the strongly acidic solutions.In typical surface waters, when the concentration of chromium is less than 5.0 μg/L, only HCrO 4 -and CrO 4 2-can be found.The soluble chromium species CrO 4 2-and Cr(OH) 3 are bio-accumulated as phyto-and zooplankton readily absorb chromium in all its forms.Nevertheless, the slow water fl ow and reducing bandwidth can cause adsorption of chromium on the surface of suspended particles in water and thus its deposition occurs.
Figure 6 shows DHCE of the chemical forms of Cr(VI) for its different total concentrations in aqueous solution.In contrast to Cr(III), DHCE for Cr(VI) are changed to a much lesser extent with the change in the total concentration of the metal ion in solution.

Conclusions
It is worthy to note that our results, based on the thermodynamic analysis and graphic design of the calculated data in the form of the diagrams of heterogeneous chemical equilibria, are in good agreement with the available experimental data.

Figure 1 .
Figure 1.The total Gibbs energy versus pH for the system "saturated aqueous solution -Cr(III) hydroxide" for different analytical concentrations of Cr(III).

Figure 2 .
Figure 2. The curves of distribution of the Cr(III) hydroxocomplexes as a function of pH for C 0 (Cr) = 10 -6 М.

Figure 5 .
Figure 5.The degree of polynuclearity of the Cr(VI) species versus pH at different analytical concentrations of Cr(VI).

Figure 6 .
Figure 6.The curves of distribution of the complexes of Cr(VI) as a function of the pH solution at different analytical concentrations of Cr(VI).